Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Ample divisors on the blow up of $\mathbf{P}^n$ at points


Author: E. Ballico
Journal: Proc. Amer. Math. Soc. 127 (1999), 2527-2528
MSC (1991): Primary 14N05; Secondary 14C20, 14M20
Published electronically: April 28, 1999
MathSciNet review: 1676319
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Fix integers $n,k,d$ with $n\ge 2,d\ge 2$ and $k>0$; if $n=2$ assume $d\ge 3$. Let $P_1,\dotsc,P_k$ be general points of the complex projective space $\mathbf{P}^n$ and let $\pi:X\to \mathbf{P}^n$ be the blow up of $\mathbf{P}^n$ at $P_1,\dotsc,P_k$ with exceptional divisors $E_i:=\pi^{-1}(P_i)$, $1\le i\le k$. Set $H:=\pi^*(\mathbf{O}_{\mathbf{P}^n}(1))$. Here we prove that the divisor $L:=dH-\sum _{1\le i\le k}E_i$ is ample if and only if $L^n>0$, i.e. if and only if $d^n>k$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 14N05, 14C20, 14M20

Retrieve articles in all journals with MSC (1991): 14N05, 14C20, 14M20


Additional Information

E. Ballico
Affiliation: Department of Mathematics, University of Trento, 38050 Povo, Trento, Italy
Email: ballico@science.unitn.it

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05401-5
PII: S 0002-9939(99)05401-5
Received by editor(s): August 10, 1997
Published electronically: April 28, 1999
Communicated by: Ron Donagi
Article copyright: © Copyright 1999 American Mathematical Society